A358984 The number of n-digit numbers k such that k + digit reversal of k (A056964) is a square.

3, 8, 19, 0, 169, 896, 1496, 3334, 21789, 79403, 239439, 651236, 1670022, 3015650, 27292097, 55608749, 234846164, 366081231, 2594727780, 6395506991

Offset: 1

Author

Nicolay Avilov, Dec 08 2022

Keywords

• nonn
• base
• more

Comments

Number of terms of A061230 which are n digits long.

Examples

			a(1) = 3 because there are 3 single-digit numbers: 0, 2, 8 such that b + b = m^2, for example, 8 + 8 = 16 = 4^2;
a(2) = 8 because there are 8 two-digit numbers: 29, 38, 47, 56, 65, 74, 83, 92 such that bc + cb = m^2, for example, 29 + 92 = 121 = 11^2.
		

Links

• Nicolay Avilov, Problem of the Moscow Mathematical Olympiad, 1945 (in Russian).
• Index to sequences related to Olympiads.
• Index entries for sequences related to Reverse and Add!

Crossrefs

Cf. A056964, A061230, A356648.

Programs

Mathematica

a[n_]:=Length[Select[Table[k, {k, 10^(n-1),10^n-1}],IntegerQ[Sqrt[#+FromDigits[Reverse[IntegerDigits[#]]]]]&]]; Array[a,10] (* Stefano Spezia, Dec 09 2022 *)

Python

from math import isqrt
def s(n): return isqrt(n)**2 == n
def c(n): return s(n + int(str(n)[::-1]))
def a(n): return 3 if n == 1 else sum(1 for k in range(10**(n-1), 10**n) if c(k))
print([a(n) for n in range(1, 7)]) # Michael S. Branicky, Dec 08 2022

Extensions

a(9)-a(10) from Michael S. Branicky, Dec 08 2022

a(11)-a(20) from Talmon Silver, Dec 25 2022